For purposes of the EIN the address is largely inconsequential. The IRS cannot (read: won't) recover the EIN if you fail to write it down after the website generates it for you. On your actual tax form the address is more consequential, and this is more so a question of consistency than anything. But an entity can purchase property anywhere and have a different address subsequent years. Paying the actual taxes means more than the semantical inconsistencies. The whole purpose of separate accounts is to make an audit easier, so even if someone imagines that some action (such as address ambiguity) automatically triggers an audit, all your earnings/purchases are not intermingled with personal stuff, which just streamlines the audit process.
Consequences (or lack thereof) aside, physical means where physical property is. So if you have an actual mailing address in your state, you should go with that. Obviously, this depends on what arrangement you have with your registered agent, if all addresses are in Wyoming then use the Wyoming address and let the Registered Agent forward all your mail to you.
Don't forget your $50 annual report in Wyoming ;)
How did you open a business paypal without an EIN? Business bank accounts? Hm... this is for liability purposes...